Articles written in Pramana – Journal of Physics

    • Inverse beta decay of arbitrarily polarized neutrons in a magnetic field

      Kaushik Bhattacharya Palash B Pal

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      We calculate the cross-section of the inverse beta decay process,ve+n → p+e, in a background magnetic field which is much smaller than mp2/e. Using exact solutions of the Dirac equation in a constant magnetic field, we find the cross-section for arbitrary polarization of the initial neutrons. The cross-section depends on the direction of the incident neutrino even when the initial neutron is assumed to be at rest and has no net polarization. Possible implications of the result are discussed.

    • An effective Hamiltonian approach to quantum random walk


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      In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltoniansare generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, $\it{Sci. Rep}$. 3, 2829 (2013)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.

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